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Displaying similar documents to “On dependent elements in rings.”

( σ , τ ) -derivations on prime near rings

Mohammad Ashraf, Asma Ali, Shakir Ali (2004)

Archivum Mathematicum

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There is an increasing body of evidence that prime near-rings with derivations have ring like behavior, indeed, there are several results (see for example [1], [2], [3], [4], [5] and [8]) asserting that the existence of a suitably-constrained derivation on a prime near-ring forces the near-ring to be a ring. It is our purpose to explore further this ring like behaviour. In this paper we generalize some of the results due to Bell and Mason [4] on near-rings admitting a special type of...

Some results of reverse derivation on prime and semiprime Γ-rings

Neshtiman Nooraldeen Suliman (2015)

Discussiones Mathematicae - General Algebra and Applications

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In the present paper, it is introduced the definition of a reverse derivation on a Γ-ring M. It is shown that a mapping derivation on a semiprime Γ-ring M is central if and only if it is reverse derivation. Also it is shown that M is commutative if for all a,b ∈ I (I is an ideal of M) satisfying d(a) ∈ Z(M), and d(a ∘ b) = 0.